Estimate the noise level distribution from noise measured at detections

Noise levels measured at detections are biased low, because detections over-represent quiet periods. This undoes that bias.

Usage

nlFromDetections(
  snrInfo,
  snrDetFun,
  SL,
  TL,
  truncationDistance = max(TL[[1]]),
  nlColumn = "NoiseRL",
  searchWidth = 25,
  ...
)

Arguments

snrInfo

Table of SNR information containing a column of noise level measurements in dB, and optionally a Detected column (see above).

snrDetFun

Detection function, as passed to pDetInArea.

SL

Source level distribution, with elements named mean and sd.

TL

Transmission loss table. First column ranges in metres, remaining columns TL in dB per radial transect.

truncationDistance

Scalar or one value per transect, in metres.

nlColumn

Name of the noise level column. Default "NoiseRL".

searchWidth

Width in dB of the interval searched above the measured mean. The bias cannot be negative, so the search runs upwards only.

...

Passed to pDetGivenNL, e.g. binWidth.

Value

Data.frame with one row and columns mean, sd and sampleSize, the same format as nlFromSnrInfo and noiseLevelDistribution.

Details

If snrInfo has a Detected column (as chtToSNRinfo's output always does), this filters to Detected == TRUE before doing anything else – the bias-correction below only makes sense applied to noise measured at detections specifically, matching this function's own name, not at every event a capture history table happens to record (which, for a table built around adjudicated ground truth rather than one detector's own raw positives, can be mostly missed events). Skipping this filter doesn't error – the uniroot search still finds a root – it just corrects a mean that's already close to unbiased as if it still needed the same correction, overshooting past the true value rather than landing on it. If no Detected column is present, snrInfo is assumed to already contain only detections (matching simulateDetectedNoise's own output, which never carries one).

Replaces nlFromSnrInfo, which corrected the same bias by adding the SNR at which the detection function reaches 0.5. That quantity is a property of the detector. The bias is a property of the propagation geometry and the noise variance. The two coincide only by chance. See the noiseLevels vignette.

The standard deviation is taken from the measurements directly. Filtering by detection shifts the mean but barely narrows the distribution, so the measured standard deviation is close to the truth even though the measured mean is not. This leaves one unknown, found by stats::uniroot.